Signal processing system for sensing a periodic signal in the presence of another interfering signal

ABSTRACT

A signal processing system, especially for use in vibration control, wherein noise-free signals inductive of the timing of a primary source and of the timing of at least one interfering secondary source of periodic vibrations are provided as inputs, together with a vibration input signal derived from a sensor sampling the vibrations, and wherein the signals are processed to produce an output representative of interference free vibration of the primary source.

FIELD OF THE INVENTION

This invention concerns a signal processing system which can be used tomonitor one substantially periodic component where there is interferencefrom one or more other substantially periodic components. Each componentis usually associated with a particular vibration source. The system maybe incorporated in an active control system for reducing noise and inthe resulting control system, is normally used one per source ofvibration.

The signal processing system has input signals which are time-related toeach of the periodic sources. These additional inputs allow improvedrejection of the vibration from other sources.

In this application the term vibration is used to mean any vibration,such as the vibration of solids and the vibration of fluids, normallyreferred to as sound or velocity perturbation.

BACKGROUND INFORMATION

There have been many attempts to achieve noise reduction by the use ofactive control and there are many publications relating to theseprevious systems. Most have dealt with the control of a single source ofunwanted vibration, while others have treated multiple sources as asingle, more complicated source. For example, in the control of cabinnoise in propeller driven aircraft, the individual propellers areseparate sources which are physically separate and, since the enginespeeds are not identical, not completely coherent. However, previousmethods to control aircraft cabin noise, have considered the vibratingcabin walls as a single, distributed source. Vide Warnaka, G. E. &Zalas, J. M. "Active Attenuation of noise in a closed structure." UKPatent 2,132,053: Groves, H. W. "Noise Suppression." UK Patent2,126,837: Nelson, P. A. & Elliott, S. J. "Improvements in or relatingto active noise reduction." UK Patent 2,149,614.

Most active control systems use a measure of the residual vibration at apoint where reduction is desired to adjust the actuator drives videChaplin, G. "Active attenuation of recurring sounds." UK Patent1,577,322. This measure will be corrupted by noise, due either toextraneous "background" vibration or to electronic noise. The level ofthis noise will limit the performance of the control system. If thesource of vibration to be controlled is periodic, or almost periodic, innature then the process of synchronous averaging can be used to rejectnoise which is not harmonically related to the vibration source. Asignal from the vibration source is needed to synchronize the averagingprocess. This may be a signal from a tachometer or an applied voltage orsimilar. If the noise is random in nature then the ratio of the signalpower to the noise power is increased in proportion to the number ofaverages. However, if the noise is from another periodic source of notidentical speed, the noise to signal ratio is an oscillating function ofthe averaging time. Reference is made to FIG. A of the drawings, inwhich the envelope decays only slowly and scales with the best period ofthe two periodic sources. Conventional active control means then adoptone of two strategies.

The first is to average for a sufficiently long time, compared with thebeat period, so that the envelope of the noise to signal ratio hasdecayed to a small enough value.

The second is to treat the vibration as if it were coming from a singlesource. This requires the system to adapt on a time-scale short comparedwith the beat period.

The first method cannot be used if the signal, that is the unwantedvibration, is not constant for long enough. The second method fails ifthe two fundamental frequencies drift apart producing a very rapidbeating.

SUMMARY OF THE INVENTION

In a system incorporating the invention separation of the signal fromthe noise can be achieved by averaging for just the right period of timeso that the noise to signal ratio is at, or close to, a zero.

The invention also lies in a signal processing means which achieves thisseparation, and which is characterized by having at least two inputs(rather than the single input of a conventional system), so that thesystem is supplied with information as to the timing of the secondarysource or sources as well as the primary source.

An example of such a signal processing system incorporated in an activecontrol system comprises a controller having as inputs, a signal S₁which is time related to the vibration to be controlled, a signal S₂which is time related to the vibration of a secondary source, and errorsignals which characterize the residual vibration, wherein the inputsignals are processed to produce output signals which are fed to anactuator system to produce a control vibration.

If the error signals y(t) can each be considered as being composed oftwo sinusoidal components y₁ (t) and y₂ (t) having repeat periods T₁ andT₂, the task of the signal processor of the invention is first todetermine the component y₁ (t). This is achieved by means of atransducer (e.g. a tachometer) associated with the source of the firstvibration to give a measure of its period T₁. By sampling the signaly(t) (=the combination of the two input signals) of the same point inevery cycle of the primary vibration, it can be shown that if the twoperiods T₁ and T₂ are similar, the phase of the second component changesthrough 360° during N=T₂ /(T₁ -T₂) cycles.

If the average of N samples is taken, it thus approximates to y₁ (t)since the components introduced by y₂ (t) during that same N cycles willhave effectively summed to zero.

Thus for the invention to be put into effect it is necessary for theprocessor to know the repeat period T₂ of the second component, so thatthe value of N for any given T₁ can be calculated, thus enabling theaveraging period (number of samples, if one per cycle) to be determined.

The invention can thus handle any periodic signals since any such signalcan be thought of as being composed of a sum of sinusoidal components ofappropriate amplitude and phase.

The invention can also handle signals whose frequencies are slowlychanging.

The invention can be stated as comprising signal processing means forsensing the vibration from a primary source of periodic vibration in thepresence of interference from one or more secondary sources of periodicvibration, in which the signal processing means has a noise-free inputfrom each source of periodic vibration which gives the signal processingmeans information about the timing of vibration, and a vibrationinput-signal that senses both primary and secondary vibration, furthercharacterized in that the signal processing means produces an outputdetermined from the inputs representative of the vibration from theprimary source with a minimum of interference from the secondary sourceof sources.

A processing means embodying the invention uses the noise-free inputfrom the primary source of vibration to set the time base for samplingthe vibration signal.

The invention also envisages signal processing means in which thesampled vibration input signal is averaged over a number, M, of periodsof the primary source of vibration and the number, M, is determined fromthe length of the primary and secondary vibration periods.

The invention also envisages a signal processing means in whichdifferent weighting is given to each set of samples of the vibrationinput signal taken in one period of the primary source of vibration.

Preferably the weighting is adjusted to minimize the noise amplificationwhile maintaining the measurement of the primary vibration undistortedand maintaining the total rejection of the secondary vibration.

The weighting is conveniently adjusted to minimize jointly the noiseamplification and the response to the secondary vibrations whilemaintaining the measurement of the primary vibrations undistorted.

The invention also lies in a vibration control system used to controlthe sound from a primary source of periodic vibration by drivingactuators which introduce the controlling vibration, and sensors areprovided which are responsive to the resultant controlled vibrations incombination with a signal processing means as aforesaid.

Two or more vibration control systems may be provided where each one isused to control the vibration from one of the sources of periodicvibration.

Such a vibration control system can provide an output or outputs equalto or representative of the current estimate of the residual primaryvibration component of the vibration input signal or signals.

The input signals for such a vibration control system convenientlycomprise (or are representative of) the current estimate of the residualsecondary vibration component of the vibration input signal.

Two or more vibration control systems as aforesaid may be connected sothat they exchange information about their estimates of the residualvibrations.

A vibration control system in accordance with the invention may alsoprovide an output which indicates the phase of its adaption cycle.

A vibration control system in accordance with the invention may includean input which indicates the phase of adaption of other control systemsoperating upon or affecting the vibration input signals, and may usethis input to synchronize its adaption cycle to minimize errors.

Two or more vibration control systems as aforesaid may be connected sothat they exchange information about the adaption timing.

The invention also lies in the mounting of a vibration control system orsystems according to the invention so as to reduce the internal noise inan enclosed space such as in an aircraft cabin or a machinery room of aship.

The invention also lies in the mounting of a vibration control system orsystems according to the invention so as to reduce the vibrationproduced by one or more sources mounted on a common structure forexample in the propulsion system of a submarine or ship, or the fuselageof an aircraft.

The invention also lies in the mounting of a vibration control system orsystems according to the invention so as to reduce the vibrationproduced by one or more sources connected in a ducting system forexample where two fans pump air in series.

The invention may also be employed in signal processing means used toreduce the effect of an electrical supply mains induced interference.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will now be described by way of example with reference tothe accompanying drawings, in which:

FIG. 1A shows a decaying noise envelope

FIG. 1 shows how sampling components vary from cycle to cycle, when acomposite signal is regularly sampled,

FIG. 2 shows a basic active noise control system incorporating a signalprocessing system in accordance with the invention,

FIG. 3 shows how by using two controllers so different components can beisolated from the composite signal to drive actuators, and

FIG. 4 is an example of a signal processing system embodying theinvention.

DESCRIPTION OF SYSTEMS EMBODYING THE INVENTION

An example of such a signal processing system incorporated in an activecontrol system in FIG. 2. The controller, C₁, has, as inputs, signal S₁which is time related to the vibration to the controlled, signal S₂which is time related to the vibration of the secondary source, andsignals which characterise the residual vibration. These input signalsare processed to produce the output signals X₁ which are fed to theactuator system. The actuator system produces the control vibrations.

As a simple example of the signal processing used by the system we canconsider a signal y(t) at time t which is composed of two sinusoidalcomponents, y₁ (t) with amplitude A and repeat period T₁ and y₂ (t) withamplitude B and repeat period T₂. The signal is

    y(t)=A sin (2πt/T.sub.1)+B sin (2πt/T.sub.2)

The two components of the signal are shown in FIG. 1. The task of thesignal processor is to determine the first component y₁ (t)=A sin(2πt/T₁). One way of doing this is as follows: A tachometer or othersensor is connected to the source of the first vibration and provides ameasurement of its period T₁. The signal processor examples the signaly(t) once every cycle. After n cycles the signal is

    y(t+nT.sub.1)=A sin (2πt/T.sub.1 +2n π) +B sin (2πt/T.sub.2 +2nπ(T.sub.1 -T.sub.2)/T.sub.2 +2nπ)

where we have used the identity ##EQU1## We can also use the identity##EQU2##

Thus, the contribution from the first component is the same everysample, while the contribution from the second component varies fromsample to sample. This is shown in FIG. 1. If the two frequencies areclose together than (T₁ -T₂)/T₂ is small. The phase of the secondcomponent changes by an amount 2π(T₁ -T₂)/T₂ radians between eachsample, therefore when N(T₁ -T₂)/T₂ ≃1 the phase will have changed by 2πradians or 360° This is after N=T₂ /(T₁ -T₂) cycles or a time ##EQU3##which corresponds to half the `beat` period of the two signals. If wetake the average of the N samples we get ##EQU4## since thecontributions from the second component tend to cancel each other out.Thus if we average over just the right number of samples we can obtain agood estimate of y₁ (t). In order to calculate thee right number thesignal processor must known the repeat period, T₂, of the secondcomponent which it obtains from a second tachometer or sensor.

This method can be extended to cope with generally periodic signalssince each can be thought of as being composed of a sum of sinusoidalcomponents with the appropriate amplitude and phase. It can also beextended to cope with signals whose frequencies are slowly changing.

We will now explain how the signal processing system of the inventionachieves its aim more generally by resorting to some mathematicalanalysis. Suppose the vibration to cancelled produces a signal y(t) attime t from one of the sensors. This signal is composed of a signals y₁(t) due to the first source, y₂ (t) due to the secondary source and anoise component n(t) due to background vibration and electrical noise.

In order to simplify the explanation that follows y₁ (t) and y₂ (t) areassumed to be periodic for the duration, MT₁, of the measurement so that

    y.sub.1 (t)=y.sub.1 (t+nT.sub.1) for 0<n<M                 (3.1)

    y.sub.2 (t)=y.sub.2 (t+mT.sub.2) for 0<mT.sub.2 <MT.sub.1  (3.2)

where T₂ and T₂ are the periods of the signals y₁ and y₂ respectively.By the usual process of Fourier analysis the signal can be decomposedinto harmonic components ##EQU5## where a_(n), b_(n), α_(n) and β_(n)are real coefficients.

The signal y(t) is sampled in synchronism with a signal from the firstsource which has the period T₁. The M samples can be written as a vector

    Y={y(t),y(t+T.sub.1),y(t+2T.sub.1), . . . y(t+(M-1)T.sub.1)}(3.5)

We can introduce vectors associated with various harmonic components ofthe second source, namely ##EQU6## we can set α₀ =O without loss ofgenerality.

Similarly we can write ##EQU7##

The signal processing system forms the linear combination of the signalsamples ##EQU8## where t_(q) is the time of the k-th sample in theprimary signal's period. Q is the number of samples in each period.

In the most straight forward case the signal processing system forms theaverage of the sampled signals ##EQU9##

The simplest approach is to set ##EQU10## so that ##EQU11##

The form of (W^(T) c_(n))² is shown in FIG. A, as a function of theaveraging time MT₁ while ##EQU12##

When the periods T₁ and T₂ are similar the cosine is a slowly varyingfunction of m and the summation can be approximated by an integral. Inparticular ##EQU13##

Therefore W^(T) c_(n), and W^(T) s_(n) are all zero when ##EQU14##

The factor ##EQU15## is unlikely to be an integer so that the squarebrackets denote that the closest integer value should be taken.

We can now see that when the system averages the input signals for Mperiods the other signal would be rejected since W^(T) c and W^(T) s arethen both zero.

The factor ##EQU16## is plotted as a function of T/T₂ in FIG. A; theenvelope, given by ##EQU17## is also shown.

One way of finding the appropriate time for averaging is to generate thediscrete functions c₁ and s₁ and average these until both averages arezero or change sign together. Alternatively the system could look atalternate zero crossings of the average of c₁ or s₁. There are a varietyof ways of finding the appropriate average time.

A control system can also be applied to the secondary source or sources.In order to discriminate against the vibration due to the first source(and the first control system) it too will require a second input toenable it to average for the appropriate number of cycles. The sensorsand actuators could be common to both systems.

In practice the signal received from the sensor will be composed ofcomponents due to the sources and to noise and also to the controlvibrations produced by the actuators. Thus, for each controller, theaveraging process described above will produce an estimate of thesignals due to any uncontrolled vibration from the corresponding source.These estimates could converted to analogue form and subtracted from theinputs to the other controller, either before or after digital sampling.This process requires the provision of two sets of Digital to AnalogueConverters (D.A.C's) for each controller. One set produces actuatordrive signals, x₁, the other set produces the estimated signal ε₁, dueto the uncontrolled vibration from one source. An example of such asystem for controlling two sources is shown in FIG. 3.

This process has the potential of reducing the component of periodicnoise and thus permitting greater reduction of the background noise.Care must be taken, however, that the estimates are accurate enough toavoid an unstable accumulation of errors.

Just such an accumulation occurs when the two periods are identical, butit may be tolerated if the periods are continually changing.

An example of the use of this approach is the control of sound in thecabin of a propeller driven aircraft. The propellers are usuallydesynchronized but the fundamental frequencies of the blade passing areusually separated by less than a few Hertz. This means that aconventional system would need to average for many seconds to separateout the two fundamental tones or would need to adapt many times a secondto control the higher harmonics.

A system using the method of this invention could comprise a sensor,such as a tachometer, on each propeller or engine to give its positionin the cycle, a set of microphones and a set of loudspeakers inside thecabin and two control systems as shown in FIG. 3. Each control systemsends out signals in synchrony with the primary tachometer input andadjusts those signals, or the way in which they are determined, on thebasis of signals obtained from the microphone array. The signals fromthe microphones are synchronously averaged for a time determined by thetwo tachometer signals.

Further information, such as the times when changes to the outputsignals are made, may be passed between the systems to improve theadaption.

If the noise is Gaussian, with power n², then the expected value of thesquare of the processed signal is ##EQU18## so the signal to noise ratioincreases with the number of averages.

An example of this signal processing system is shown in FIG. 4. Thenoise-free signal (1) from the secondary source is passed through alow-pass filter (2) and then sampled by an Analogue to Digital Converter(ADC) (3). This ADC is triggered by the noise-free signal (4) from theprimary source. The output (5) from the ADC is a linear combination ofs₁ and c₁. This output is summed in an accumulator (6). A computer (7)counts the number of accumulations and checks for sign changes in theaccumulation. At the second sign change it resets the accumulator (6) tozero, takes the outputs of the accumulator (8), divides each output bythe number of accumulations (9) and copies the results to a memorydevice (10). The vibration input signal (11) is sampled by an ADC (12)which is triggered Q times per cycle by the noise-free primary input(13). This produces Q outputs per cycle which are separately summed bythe accumulator (8). The memory device (10) could feed a Digital toAnalogue Converter, triggered by the primary noise-free input (13), sothat a continuous estimate of the primary vibration signal is available.

There is no reason however that a uniformly weighted average needs to beemployed. In fact, a non-uniform weighting may be essential if thefrequencies are changing significantly on the scale of a beat period. Inthis case the vectors s_(n) and c_(n) again contain sine and cosineterms, but the phases are determined from the phase differences betweenthe two trigger signals.

In fact discrimination against the second source can be achieved in ashorter time if a non-uniform weighting is used. We will now describe,in mathematical terms, one way to calculate the non-uniform weighting.We notice however that the contribution from Gaussian noise ismultiplied by the factor (W^(T) W)^(1/2). We therefore require that

    W.sup.T c.sub.1 =W.sup.T s.sub.1 =0, W.sup.T u=1

and that W^(T) W is as small as possible.

Hence we seek to minimise

    E=1/2W.sup.T W+(W.sup.T C-F.sup.T)λ                 (3.21)

where

C is the matrix formed by the column vectors (u, c₁,c₂ . . . ,c_(l),s_(l)). l, which must be less than half the number of samples, Q,is the number of harmonics to be discriminated against.

F is the column vector {1,0,0, . . . ,0}^(T) which contains 2l zeros. λis a vector of Lagrange multipliers. The weighting vector W whichminimizes W^(T) W subject to the constraint W^(T) C=F^(T) is

    W=C(C.sup.T C).sup.-1 F                                    (3.22)

The minimum value is

    W.sup.T W=F.sup.T (C.sup.T C).sup.-1 F                     (3.23)

which is the top left-hand element of (C^(T) C)⁻¹. This gives theamplification of the noise. If the two source periods are very closetogether then (C^(T) C) may be ill-conditioned and noise amplificationunacceptably large.

Instead we could minimise the level of the noise contamination and theother signal contamination, this would be done by minimizing

    E.sub.1 =1/2μW.sup.T DD.sup.T W+1/2W.sup.T W+λ(W.sup.T u-1) (3.24)

where D is the matrix (c₁, s₁, c₂, s₂, . . . c_(l), s_(l)) and λ is aLagrange multiplier. The constant μ represents the relative importanceof the background noise and the secondary periodic noise term.

The weight vector which minimizes E₁ is ##EQU19## where I is theidentity matrix

An example of this processing system is shown in FIG. 5. the noise-freeinputs (1) and (2) from the primary and secondary sources are fed to aTTL pulse generator which produces a once-per-cycle pulse for thesecondary source (4) and both once-per-cycle and Q-times per cyclepulses for the primary source (5). The time between each once-per-cyclepulse is measured using an internal clock pulse (6) to give the periodsT₁ and the T₂ of the primary and secondary vibrations. These are fed toa microprocessor (7) which calculates the weight vectors given by (3.21)or (3. 24). These can be calculated directly or recursively. Theseweights are then stored in a memory device (8). The once-per-cycle pulseand the Q-times per-cycle pulse from the primary source (5) are used totrigger an Analogue to Digital Converter (9) which samples the vibrationinput signal ε(t) (10). These samples are stored in a memory device(11), which may be a first-in first-out device for example. Thesesamples are then multiplied by the appropriate weights at (12) andsummed in an accumulator (13) to give an estimate of that part of thevibration input signal that is due to the primary source. After theappropriate number of accumulations determined by a counter (14) theaccumulator is reset to zero.

If the two periodic vibrations contain higher harmonics of thefundamental frequency then it is possible that the n-th harmonic of oneis very close to the m-th harmonic of the other. The difference infrequencies of these two, or any two harmonics can be used to determinethe optimal time for averaging.

It is claimed:
 1. A method of monitoring a first substantially periodic signal component of a compound signal which includes a second substantially periodic signal component, wherein the first and second signal components have separate sources, comprising the steps of:(a) sensing the first and second signal components respectively; (b) determining a beat period as a function of the sensed first and second signal components; (c) sampling the compound signal in synchronism with the first signal component; and (d) averaging the compound signal samples over a period determined by said beat period to produce a contribution signal as a function of a contribution made to the compound signal by the first signal.
 2. A method according to claim 1, wherein the beat period is defined by the product of the periods of the first and second signal components divided by the magnitude of the difference between the periods of the first and second signal components.
 3. A method of at least partially cancelling a compound signal including a first substantially periodic signal component and a second substantially periodic signal component, wherein the first and second signal components have separate sources, including the steps of:(a) Monitoring the first signal component by performing the steps:(i) sensing the first and second signal components respectively; (ii) determining a beat period as a function of the sensed first and second signal components; (iii) sampling the compound signal in synchronism with the first signal component; and (iv) averaging the compound signal samples over a period determined by said beat period to produce a contribution signal as a function of a contribution made to the compound signal by the first signal; and (b) generating a cancelling signal to cancel the first signal component of the compound signal in dependence on said contribution signal.
 4. A method according to claim 3, including the additional steps of:(a) monitoring the second signal component by performing the steps:(i) sensing the first and second signal components respectively; (ii) determining a beat period as a function of the sensed first and second signal components; (iii) sampling the compound signal in synchronism with the first signal component; and (iv) averaging the compound signal samples over a period determined by said beat period to produce a contribution signal as a function of the contribution made to the compound signal by the first signal, as if the first signal component were the second signal component and the second signal component were the first signal component; and (b) generating a cancelling signal for cancelling the second signal component of the compound signal in dependence on said contribution signal produced as a function of the contribution made to the compound signal by the second signal.
 5. An apparatus for monitoring a first substantially periodic signal component of a compound signal which includes a second substantially periodic signal, wherein the first and second signal components have separate sources, comprising:first sensor means for sensing the first signal component before it becomes combined in the compound signal, said first sensor means having an output; second sensor means for sensing the second signal component before it becomes combined in the compound signal, said second sensor means having an output; third sensor means for sensing the compound signal, said third sensor means having an output; means for producing a controlling signal as a function of the output from the first and second sensor means; sampling means arranged to sample the output from the third sensor means in synchronism with the output of the first sampling means; and accumulator means for accumulating the compound signal samples over a period determined by the controlling signal to produce a contribution signal as a function of the contribution made to the compound signal made by the first signal component.
 6. An apparatus according to claim 5, wherein the accumulator means is included in an averaging means.
 7. An apparatus according to claim 5, wherein the means for producing a controlling signal includes a further sampling means for sampling the output of the second sensor means, said further sampling means having an output, an accumulator for accumulating the output of the further sampling means, said accumulator having an output, and a control circuit arranged to detect every second zero crossing in the output of the accumulator to produce an accumulator reset signal to reset the accumulator and the controlling signal.
 8. An apparatus according to claim 5, wherein the means for producing a controlling signal comprises a microprocessor programmed to calculate a beat period from a signal representing the period of the outputs of the first and second sensing means.
 9. An active noise cancelling apparatus including: an apparatus according to claim 6;processing means for producing a cancelling signal as a function of the contribution signal; and actuator means for producing cancelling vibrations in dependence on the cancelling signal.
 10. An apparatus including first and second apparatuses according to claim 6, wherein the first signal component of the first apparatus is treated as the second signal component by the second apparatus and the second signal component of the first apparatus is treated as the first signal component by the second apparatus.
 11. An apparatus according to claim 10, wherein the processing means carry out respective adaptive processes and include means for transferring adaptive timing information therebetween to effect synchronization of their respective adaptive processes.
 12. An apparatus according to claim 9, mounted to reduce the noise in an enclosed space.
 13. An apparatus according to claim 9, mounted to reduce vibration produced by a plurality of sources of vibration on a common structure.
 14. An apparatus according to claim 9, mounted to reduce vibration produced by a plurality of sources of vibration in a ducting system. 